In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is \textbf{shown not to} be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection ($\varepsilon\sst{p} \neq 0$) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of Chlamydia trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with Chlamydia trachomatis, (ii) Concentrating on Chlamydia trachomatis intervention controls alone (Chlamydia trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and Chlamydia trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and Chlamydia trachomatis.
Nonlinear dynamics of COVID-19 SEIR infection model with optimal control analysis
